Pluto's fly-by by the New Horizons spacecraft in July 2015 has revealed a dark reddish equatorial region, named Cthulhu, covered by a dark, non-icy material whose origin and composition have yet to be determined. It has been suggested that this material could form from the sedimentation of photochemical aerosols, originating from dissociation and ionisation processes in Pluto's high atmosphere (similarly to aerosols forming Titan's haze). This hypothesis is here further investigated by comparing New Horizons spectra collected both in the visible and the near-infrared to laboratory reflectance measurements of analogues of Pluto's aerosols (Pluto tholins). These aerosols were synthesised in conditions mimicking Pluto's atmosphere, and their optical and reflectance properties were determined, before being used in Hapke models. In particular, the single scattering albedo and phase function of Pluto tholins were retrieved through Hapke model inversion, performed from laboratory reflectance spectra collected under various geometries. From reconstructed reflectance spectra and direct comparison with New Horizons data, some of these tholins are shown to reproduce the photometric level (i.e. reflectance continuum) reasonably well in the near-infrared. Nevertheless, a misfit of the red visible slope still remains and tholins absorption bands present in the modelled spectra are absent in those collected by the New Horizons instruments. Several hypotheses are considered to explain the absence of these absorption features in LEISA data, namely high porosity effects or GCR irradiation. The formation of highly porous structures, which is currently our preferred scenario, could be promoted by either sublimation of ices initially mixed with the aerosols, or gentle deposition under Pluto's weak gravity.